Infections with Epstein-Barr virus (EBV) are associated with cancer development, and EBV lytic replication (the process that generates virus progeny) is a strong risk factor for some cancer types. Here we report that EBV infection of B-lymphocytes (in vitro and in a mouse model) leads to an increased rate of centrosome amplification, associated with chromosomal instability. This effect can be reproduced with virus-like particles devoid of EBV DNA, but not with defective virus-like particles that cannot infect host cells. Viral protein BNRF1 induces centrosome amplification, and BNRF1-deficient viruses largely lose this property. These findings identify a new mechanism by which EBV particles can induce chromosomal instability without establishing a chronic infection, thereby conferring a risk for development of tumours that do not necessarily carry the viral genome.